Eigenmath Demo

e = quote(e) -- clear e, was exponential, now elementary charge

-- E is total energy

E = hbar^2 / (2 mu a0^2) - e^2 / (4 pi epsilon0 a0)

dE = d(E,a0)

-- Bohr radius minimizes total energy

a0 = 4 pi epsilon0 hbar^2 / (e^2 mu)

"Bohr radius"

"Verify that total energy is minimized for Bohr radius (1=ok)"

dE == 0

-- base units

ampere = "ampere"
kilogram = "kilogram"
meter = "meter"
second = "second"

-- derived units

coulomb = ampere second
farad = ampere^2 kilogram^(-1) meter^(-2) second^4
joule = kilogram meter^2 second^(-2)
volt = ampere^(-1) kilogram meter^2 second^(-3)

"Numerical value for Bohr radius"

pi = float(pi)

hbar = 1.054572 10^(-34) joule second      -- Planck's constant
epsilon0 = 8.854188 10^(-12) farad / meter -- electric constant
e = 1.602176 10^(-19) coulomb              -- elementary charge
me = 9.109382 10^(-31) kilogram            -- mass of electron
mp = 1.672622 10^(-27) kilogram            -- mass of proton

mu = me mp / (me + mp)

"Numerical value for Rydberg unit of energy"

-E 1/(1.602177 10^(-19)) "electron-volt" / joule